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Combining MFS and PGD methods to solve transient heat equation

Abstract : We propose in this article a numerical algorithm based on the combination of the method of fundamental solutions (MFS) and the proper generalized decomposition technique (PGD) to solve time-dependent heat equation. The MFS is considered as a truly meshless technique well adapted for a wide range of physical problems and the PGD approach can be considered as a reduction technique based on the separated representation of the variable functions. The proposed study relates to a separation between the spatial and temporal coordinates. To show the effectiveness of the proposed algorithm, several examples are presented and compared to the reference results
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Submitted on : Tuesday, May 25, 2021 - 10:07:06 PM
Last modification on : Friday, August 5, 2022 - 2:54:00 PM



Kékéli Kpogan, Abdeljalil Tri, Amen Sogah, N. Mathieu, Hamid Zahrouni, et al.. Combining MFS and PGD methods to solve transient heat equation. Numerical Methods for Partial Differential Equations, 2018, 34 (1), pp.257-273. ⟨10.1002/num.22196⟩. ⟨hal-03235627⟩



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